According to the range rule of thumb, the standard deviation of a data set can be roughly estimated as which of the following expressions?

• A. $\frac{\mathrm{Range}}{2}$
• B. $\frac{\mathrm{Range}}{6}$
• C. $\frac{\mathrm{Range}}{4}$
• D. $\frac{\mathrm{Range}}{10}$

Answer: (C)

Verified step by step guidance

1. Understand that the range rule of thumb is a simple method to estimate the standard deviation of a data set using the range, which is the difference between the maximum and minimum values.
2. Recall that the standard deviation measures the average amount of variation or dispersion in a set of values.
3. The range rule of thumb approximates the standard deviation by dividing the range by a constant, which is chosen based on typical data distributions.
4. Recognize that the commonly used constant in this rule is 4, so the estimated standard deviation is given by the formula: \(\text{Standard Deviation} \approx \frac{\text{Range}}{4}\).
5. This formula provides a quick estimate and is especially useful when the exact standard deviation is difficult to calculate or when only the range is known.